The Tangent Line and the Derivative
I've adjusted your point from the previous activity so it leaves a breadcrumb trail. This looks a lot like the breadcrumb trail from earlier in this chapter, but now it EXACTLY matches
f'(x)=2*x+2, and isn't just close. Type f'(x)=2x+2 into the input bar again and see for yourself. Zoom way in to confirm that the breadcrumb trail is now an exact match.Before we move on, I want to make a quick note about multiplication in Geogebra. Occasionally you might see me write
f'(x)=2x+2 or you might see me write f'(x)=2*x+2. The difference of course is the "*".
To be clear: both mean exactly the same thing. Sometimes I put the "*" in to make it clear that there is a multiplication in the definition of a function. However, as you know from your earlier studies, "2x" always means "2 times x", so technically, it's redundant.
Also, the good news is that Geogebra understands both, and interprets bot "2x" and "2*x" as 2*x", but then later as they become more comfortable with the material, they get lazy, and drop the "*". Whatever works for you is fine.
Move on when you're ready.